Explain the Difference Between Greedy Algorithms and Dynamic Programming
Concept
Both Greedy algorithms and Dynamic Programming (DP) are optimization strategies used to solve problems efficiently.
However, they differ in how they approach subproblems and decision-making.
- Greedy algorithms make locally optimal choices hoping they lead to a globally optimal solution.
- Dynamic Programming explores all possibilities and stores intermediate results to ensure global optimality.
1. Greedy Algorithm Characteristics
A Greedy algorithm builds a solution step by step, always choosing the best available option at the moment without reconsidering previous choices.
Example:
Choosing the fewest coins to make change using denominations [1, 5, 10, 25].
Greedy Step (safe for MDX):
Choose the largest coin ≤ remaining amount.
Repeat until amount = 0.
Advantages:
- Simple and fast (O(n log n) or better).
- Requires less memory — no state tracking.
Limitations:
- Doesn’t always guarantee optimal solutions (depends on problem structure).
2. Dynamic Programming Characteristics
Dynamic Programming solves problems by breaking them into overlapping subproblems and combining results for the global optimum.
Example:
Coin change problem for non-standard denominations like [1, 3, 4].
Greedy fails; DP guarantees minimal coins.
DP Step (safe for MDX):
dp[i] = min(dp[i - coin] + 1) for each coin
Advantages:
- Guarantees optimal solutions.
- Works for complex dependencies (knapsack, scheduling).
Limitations:
- Higher memory and computational overhead.
- Requires clear subproblem formulation.
3. Comparison Table
| Aspect | Greedy Algorithm | Dynamic Programming |
|---|---|---|
| Decision Basis | Local optimum | Global optimum |
| Optimal Guarantee | Not always | Always (if optimal substructure) |
| Overlapping Subproblems | No | Yes |
| Memory Usage | Low | High |
| Example Problems | Huffman coding, Kruskal’s MST | Knapsack, Fibonacci, Matrix Chain |
| Implementation | Iterative | Recursive or tabulated |
4. When to Use Each
| Scenario | Recommended Approach |
|---|---|
| Problem satisfies Greedy-choice property | Use Greedy |
| Problem has overlapping subproblems and optimal substructure | Use DP |
| You can make independent local decisions safely | Use Greedy |
| You need global analysis and caching | Use DP |
5. Example Comparison — Activity Selection vs Knapsack
Activity Selection (Greedy Works)
Select maximum number of non-overlapping meetings.
Rule: Always pick the next meeting that ends earliest. Greedy works because local best (earliest end) leads to global best (max count).
0/1 Knapsack (DP Required)
Each item has weight and value — find max value without exceeding capacity. Greedy fails because you must consider combinations; DP explores all valid subsets.
6. Real-World Applications
| Domain | Greedy Example | DP Example |
|---|---|---|
| Networking | Dijkstra’s shortest path | Bellman-Ford shortest path |
| Compression | Huffman coding | LZ77 compression |
| Finance | Greedy stock selection | Portfolio optimization |
| AI / ML | Greedy search | Reinforcement learning (value iteration) |
7. Hybrid Approaches
Some algorithms combine both strategies — Greedy-DP hybrids.
Example:
- Prim’s Algorithm (Greedy) + Dynamic Relaxation (DP-like memory) in advanced routing optimizations.
- A* search uses greedy heuristics + DP-like cost accumulation.
8. Interview Tip
- Mention Greedy-choice property and Optimal substructure explicitly.
- Use examples where greedy fails (e.g., coin change with [1, 3, 4]).
- Contrast simplicity (Greedy) vs completeness (DP).
- Draw parallels with business trade-offs — fast vs perfect.
Summary Insight
Greedy algorithms optimize for now; Dynamic Programming optimizes for later. The right choice depends on whether local shortcuts lead to global success.